Bounding Techniques and Their Application to Simplified Plastic Analysis of Structures

  • T. Panzeca
  • C. Polizzotto
  • S. Rizzo
Part of the International Centre for Mechanical Sciences book series (CISM, volume 299)


In the framework of the simplified analysis methods for elastoplastic analysis problems, the bounding techniques possess an important role. A class of these techniques, based on the so-called perturbation method, are here presented with reference to finite element discretized structures. A general bounding principle is presented and its applications are illustrated by means of numerical examples.


Deformation Measure Residual Displacement Basic Load Perturbation Vector Shakedown Analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Capurso, M., Corradi, L., and Maier, G.: Bounds on deformations and displacements in shakedown theory, in: Proc. of the Seminar on Materials and Structures under cyclic loads, Laboratoire de Mécanique des Solides, Ecole Polytechnique, Palaiseau, (France), Sept. 28 and 29, 1978, 231–244.Google Scholar
  2. 2.
    Leckie, F.A.: Review of bounding techniques in shakedown and ratchet-. ting at elevated temperature, Welding Research Council Bullettin, 195, (1974), p. 1.Google Scholar
  3. 3.
    Ponter, A.R.S.: An upper bound on the small displacements of elastic, perfectly plastic structures, J. Appl. Mech., 39, (1972), 959–963.CrossRefGoogle Scholar
  4. 4.
    König, J.A., and Maier, G.: Shakedown analysis of elastoplastic structures: a review of recent developments, Nucl. Engrg. Des., 66, (1981), 81–95.Google Scholar
  5. 5.
    Ponter, A.R.S.: General displacement and work bounds for dynamically loaded bodies, J. Mech. Phy. Solids, 23, (1975), 157–163.MathSciNetGoogle Scholar
  6. 6.
    König, J.A.: On some recent developments in the shakedown theory, Advances in Mechanics, 5, (1982), 237–258.MathSciNetGoogle Scholar
  7. 7.
    Polizzotto, C.: Bounding principles for elastic-plastic-creeping solids loaded below their shakedown limits, Meccanica, 17, (1982), 143–148.CrossRefMATHGoogle Scholar
  8. 8.
    Polizzotto, C.: On shakedown of structures under dynamic agencies, in: Inelastic structures under variable loads, (eds. C. Polizzotto and A. Sawczuk ), Cogras, Palermo, (1984), 5–29.Google Scholar
  9. 9.
    Polizzotto, C.: A unified treatment of shakedown theory and related bounding techniques, SM Archives, 7, (1982), 19–75.MATHGoogle Scholar
  10. 10.
    Polizzotto, C.: A bounding technique for dynamic plastic deformations of damped structures, Nucl. Engrg. Des., 79, (1984), 363–376.Google Scholar
  11. 11.
    Polizzotto, C.: Deformation bounds for elastic-plastic solids within and out of the creep range, Nucl. Engrg. Des., 83, (1984), 293–301.Google Scholar
  12. 12.
    Argyris, J.H.: Continua and Discontinua, Proc. 1st. Conf. on Matrix Methods in Structural Mechanics, Wright Patterson Air Force Base, Dayton, Ohio, (1965).Google Scholar
  13. 13.
    Corradi, L.: On compatible finite element models for elastic plastic analysis, Meccanica, 13, (1978), 133–150.CrossRefMATHGoogle Scholar
  14. 14.
    Panzeca, T., and Polizzotto, C.: A finite element model for dynamic elastoplastic analysis, in: Computational Plasticity, (ed. by D.R.J. Owen, E. Hinton, E. Onate), Pineridge Press, Swansea, U.K. (1987), Vol. II, 1247–1262.Google Scholar
  15. 15.
    Martin, J.B.: Plasticity: Fundamentals and General Results, The MIT Press, Cambridge Mass., (1975).Google Scholar
  16. 16.
    Koiter, W.T.: General theorems of elastic-plastic solids, in: Progress in Solid Mechanics, (eds. I.N. Sneddon and R. Hill), North-Holland, Amsterdam, (1964), Vol. 1, 167–221.Google Scholar
  17. 17.
    Maier, G.: Piecewise linearization of yield criteria in structural plasticity, SM Archives, 1, (1976), 239–281.Google Scholar
  18. 18.
    Cohn, M.Z, and Maier, G., (eds.): Engineering Plasticity by Mathematical Programming, Pergamon Press, (1978).Google Scholar
  19. 19.
    Fiacco, A.V., and McCormik, G.P.: Nonlinear programming sequential unconstrained minimization techniques, J. Wiley, New York, (1968).Google Scholar
  20. 20.
    Best, M.J., and Bowler, A.T.: ACDPAC: A Fortran - IV subroutine to solve differentiable mathematical programmes, University of Waterloo, Canada, (1978).Google Scholar
  21. 21.
    Hadley, G.: Linear Programming, Addison -Wesley, Reading, Mass. (USA), (1962).Google Scholar
  22. 22.
    Rizzo, S., and Giambanco, F.: Shakedown analysis of limited-ductility structures, Meccanica, 19, (1984), 151–157.CrossRefGoogle Scholar
  23. 23.
    Rizzo, S.: Shakedown analysis of discrete elastic-workhardening structures with displacement constraints, Proc. of SMIRT-7, Struct. Mech. in Reactor Techn., Chicago (USA), 22–26 Aug. 1983, Paper L 9–2.Google Scholar
  24. 24.
    Mazzarella, C., and Panzeca, T.: The safety factor of shell structures under variable loads with constraints on deformations, Proc. of the Euromech Coll. on Inelastic Structures under Variable Loads, Palermo, Italy, 10–14 Oct., 1983, 435–450.Google Scholar
  25. 25.
    Land, A., and Powell, S.: Fortran codes for mathematical programming, J. Wiley, New York, (1973).Google Scholar
  26. 26.
    IBM–Progr., Rod SH 20–0968–1, Mathematical Programming System Extended (MPSX), ‘and Generalized Upper Bounding (GUB), Program Description, (1972).Google Scholar
  27. 27.
    Nguyen Dang Hang, Aspects of analysis and optimization of structures under proportional and variable loadings, Eng. Opt., 7, (1983), 35–57.Google Scholar
  28. 28.
    Mazzarella, C.: I domini di plasticizzazione per le lastre formate da materiale con limiti plastici a trazione ed a compressione diversi in condizione di simmetria radiale, Giornale del Genio Civile, Fasc. 8, (1967), 511–523.Google Scholar

Copyright information

© Springer-Verlag Wien 1990

Authors and Affiliations

  • T. Panzeca
    • 1
  • C. Polizzotto
    • 1
  • S. Rizzo
    • 1
  1. 1.University of PalermoPalermoItaly

Personalised recommendations